Find the sum:
`5/(12)+7/(16)`

Answer

To find the sum of the fractions \( \frac{5}{12} + \frac{7}{16} \), we will follow these steps:

### Step 1: Find the LCM of the denominators
The denominators are 12 and 16. We will find the least common multiple (LCM) of these two numbers.

- **Prime factorization of 12**:
\[ 12 = 2^2 \times 3 \]
- **Prime factorization of 16**:
\[ 16 = 2^4 \]

To find the LCM, we take the highest power of each prime factor:
- For 2, the highest power is \( 2^4 \).
- For 3, the highest power is \( 3^1 \).

Thus, the LCM is:
\[ LCM = 2^4 \times 3^1 = 16 \times 3 = 48 \]

### Step 2: Convert each fraction to have the same denominator
Now we will convert both fractions to have the common denominator of 48.

- For \( \frac{5}{12} \):
\[ \frac{5}{12} = \frac{5 \times 4}{12 \times 4} = \frac{20}{48} \]

- For \( \frac{7}{16} \):
\[ \frac{7}{16} = \frac{7 \times 3}{16 \times 3} = \frac{21}{48} \]

### Step 3: Add the fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{20}{48} + \frac{21}{48} = \frac{20 + 21}{48} = \frac{41}{48} \]

### Final Answer
The sum of \( \frac{5}{12} + \frac{7}{16} \) is:
\[ \frac{41}{48} \]

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